t^l 



II. On a remarkable Application of Cotes* s Theorem. By}. F.W. 

 Herschel, Esq. Communicated by W. Herschel, LL.D, 

 F.R.S. 



Read November 12, 1812. 



LjET a represent the semi-transverse axis of a conic section, 

 ae the eccentricity, and consequently a (i-^e^) =:p the semi- 

 parameter. 



Let also x = . and x'= . 



r^^^ = the distance between a point in the curve, and the 

 focus, which, for distinction's sake, we shall call the first 

 focus, and the adjacent vertex the first vertex : the others the 

 second. 



/^^ = the distance between the same point and the second 

 focus. 



R = its distance from the centre. 



p = its distance from the first vertex. 



9 = the angle contained between the /* , and the prolonga' 

 tion of a line joining the first vertex and focus. 



(p = the angle contained between the R and a line joining 

 the first vertex and centre. 



^ = the angle contained between the p and the same line. 



tan. i ^ = v^IHZ . cot. X fl = l=i . cot. i fl = v/~i . 1=^ . cot. i«. 



is the angle whose supplement is, in physical astronomy, 

 known by the name of " true anomaly,'' and isr is the corre- 

 sponding *' eccentric anomaly." 



